It is a well-known fact that speakers are often oblivious of the constituent structure of historically compound words when the constituents lose currency with the passage of time, and that this process may give rise to a (mistaken) new pronunciation alongside the traditional one. This is in fact what has happened to the verb lambaste, which is now often pronounced /læmˈbæst/ instead of /læmˈbeɪst/. Moreover, the new pronunciation has been codified by all contemporary dictionaries in the form of an orthographic doublet, lambast.
The meaning given by the Oxford English Dictionary Online is “To beat soundly; to thrash; to ‘whack’. Now colloq. or vulgar.” As to the etymology, it is cited with a question mark: “? < lam v.+ baste v.3.” Both lam and baste, for that matter, share a meaning, viz. ‘whip, beat, flog,’ and the only pronunciation of baste is, of course, /beɪst/.
Neither of the two historical constituents of lambaste with the meaning of beating or flogging is in current use, hence their fading and oblivion in the compound, which then can be taken to license the mispronunciation. The latter is currently the more frequently one, at least in American English.
As is so often the case with all the traditional linguistic patrimony, ‘bad money drives out good’; or as they say in Japanese, akka wa ryooka o kuchiku suru (悪貨は良貨を駆逐する).